Download Quadratics Applications NOTES

Steps to solving a word
problem

Identify the ‘unknown’ – Let it be represented
by a letter (x, y, a etc…)

Form the quadratic equation using the given
information

Solve the equation

Check if your solutions satisfy the problem.
Example 1
The length and width of a rectangle are
(3x + 1) and (2x – 1) cm respectively. If the area
of the rectangle is 144 cm2, find x.
(3x  1)(2 x  1)  144
6 x  3 x  2 x  1  144
2
6 x 2  x  145  0
(6 x  29)( x  5)  0
Identify the unknown!
Form the equation!
Solve!
29
x  5 or  (rej)
6
Ans : x  5
Are both answers acceptable?
Example 2
The sum of the squares of 2 consecutive
positive even numbers is 580. Find the numbers
.
Identify the unknown:
Let one number be x, therefore 2nd number is x + 2
x 2  ( x  2)2  580
x 2  x 2  4 x  4  580
Form the equation
2 x 2  4 x  576  0
x 2  2 x  288  0
( x  16)( x  18)  0
x  16 or  18 (rej)
Are both answers acceptable?
Solve!
Ans :The numbers are 16 and 18
Example 3
The perimeter of a rectangle is 44 cm. The area
of the rectangle is 117 cm2. Find the length of
the shorter side of the rectangle.
Let one side be x, therefore other side is (44 − 2x) ÷ 2
= 22 – x
x(22  x)  117
22 x  x 2  117
x
x 2  22 x  117  0
( x  9)( x  13)  0
x  9 or 13
Are both answers acceptable?
Ans : The shorter side is 9 cm
x
Example 4
A rectangular swimming pool measures 25 m by 6 m. It is
surrounded by a path of uniform width. If the area of the
path is 102 m2, find the width of the path.
Let the width be x. Therefore, length of path = 25 + 2x,
breadth of path = 6 + 2x
Area of pool = 25 x 6 = 150 m2
(25  2 x)(6  2 x)  252
150  50 x  12 x  4 x 2  252
25 + 2x
6 + 2x
4 x 62 x  102  0
2
2 x 2  31x  51  0
( x  17)(2 x  3)  0
25 m
6m
Ans: The width of the path is 1.5 m
x  1.5 or -17(rej)